This document discusses image thresholding techniques for image segmentation. It describes thresholding as the basic first step for segmentation that partitions an image into foreground and background pixels based on intensity value. Simple thresholding uses a single cutoff value but can fail for complex histograms. Adaptive thresholding divides an image into sub-images and thresholds each individually to handle varying intensities better than simple thresholding. The document provides examples and algorithms to illustrate thresholding and its limitations and adaptations.

1. Digital Image Processing
Image Segmentation:
Thresholding

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Contents
Today we will continue to look at the problem
of segmentation, this time though in terms of
thresholding
In particular we will look at:
– What is thresholding?
– Simple thresholding
– Adaptive thresholding

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Thresholding
Thresholding is usually the first step in any
segmentation approach
We have talked about simple single value
thresholding already
Single value thresholding can be given
mathematically as follows:






T
y
x
f
if
T
y
x
f
if
y
x
g
)
,
(
0
)
,
(
1
)
,
(

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Thresholding Example
Imagine a poker playing robot that needs to
visually interpret the cards in its hand
Original Image Thresholded Image

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But Be Careful
If you get the threshold wrong the results
can be disastrous
Threshold Too Low Threshold Too High

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Basic Global Thresholding
Based on the histogram of an image
Partition the image histogram using a single
global threshold
The success of this technique very strongly
depends on how well the histogram can be
partitioned

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Basic Global Thresholding Algorithm
The basic global threshold, T, is calculated
as follows:
1. Select an initial estimate for T (typically the
average grey level in the image)
2. Segment the image using T to produce two
groups of pixels: G1 consisting of pixels
with grey levels >T and G2 consisting
pixels with grey levels ≤ T
3. Compute the average grey levels of pixels
in G1 to give μ1 and G2 to give μ2

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Basic Global Thresholding Algorithm
4. Compute a new threshold value:
5. Repeat steps 2 – 4 until the difference in T
in successive iterations is less than a
predefined limit T∞
This algorithm works very well for finding
thresholds when the histogram is suitable
2
2
1 
 

T

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Thresholding Example 1
Images
taken
from
Gonzalez
&
Woods,
Digital
Image
Processing
(2002)

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Thresholding Example 2
Images
taken
from
Gonzalez
&
Woods,
Digital
Image
Processing
(2002)

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Problems With Single Value
Thresholding
Single value thresholding only works for
bimodal histograms
Images with other kinds of histograms need
more than a single threshold
Images
taken
from
Gonzalez
&
Woods,
Digital
Image
Processing
(2002)

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Problems With Single Value
Thresholding (cont…)
Let’s say we want to
isolate the contents
of the bottles,
Think about what the
histogram for this
image would look like,
What would happen if we used a single
threshold value?
Images
taken
from
Gonzalez
&
Woods,
Digital
Image
Processing
(2002)

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Single Value Thresholding and
Illumination
Uneven illumination can really upset a single
valued thresholding scheme
Images
taken
from
Gonzalez
&
Woods,
Digital
Image
Processing
(2002)

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Basic Adaptive Thresholding
An approach to handling situations in which
single value thresholding will not work is to
divide an image into sub images and
threshold these individually
Since the threshold for each pixel depends
on its location within an image this technique
is said to adaptive

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Basic Adaptive Thresholding Example
The image below shows an example of using
adaptive thresholding with the image shown
previously
As can be seen success is mixed
But, we can further subdivide the troublesome
sub images for more success

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Basic Adaptive Thresholding Example
(cont…)
These images show the
troublesome parts of the
previous problem further
subdivided
After this sub division
successful thresholding
can be
achieved

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Summary
In this lecture we have begun looking at
segmentation, and in particular thresholding
We saw the basic global thresholding algorithm
and its shortcomings
We also saw a simple way to overcome some
of these limitations using adaptive thresholding